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Updated: Sep 22, 2025

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Unified View on the Mean-Field Order of Coil-Globule Transition
1Department of Chemical and Biological Engineering, Colorado State University, Fort Collins, Colorado 80523-1370, United States.
Abstract:
It is concluded that the mean-field coil-globule transition of a polymer chain of finite length N immersed in a small-molecule solvent exhibits the type-I behavior; that is, it is either a first-order phase transition, a critical point, or a crossover depending on the location of the critical point. It becomes a second-order phase transition with respect to the solvent equality characterized by the Flory-Huggins parameter χ (or equivalently the second virial coefficient υ or the temperature T) only in the limit of N → ∞. Even in this limit, it still has the type-I behavior with respect to υN1/2 (or equivalently (1 - 2χ)N1/2).
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